The invention is related to the field of doubly-resonant Kerr cavities, and in particular to nonlinear harmonic generation and devices in doubly-resonant Kerr cavities.
Nonlinear frequency conversion has been commonly realized in the context of waveguides, or even for free propagation in the nonlinear materials, in which light at one frequency co-propagates with the generated light at the harmonic frequency. A phase-matching condition between the two frequencies must be satisfied in this case in order to obtain efficient conversion. Moreover, as the input power is increased, the frequency conversion eventually saturates due to competition between up and down conversion. Frequency conversion in a doubly resonant cavity has three fundamental differences from this familiar case of propagating modes.
First, light in a cavity can be much more intense for the same input power, because of the spatial (modal volume V) and temporal (lifetime Q) confinement. We show that this enhances second-harmonic (χ(2)) conversion by a factor of Q3/V and enhances third-harmonic (χ(3)) conversion by a factor of Q2/V. Second, there is no phase-matching condition per se for 100% conversion; the only absolute requirement is that the cavity support two modes of the requisite frequencies. However, there is a constant factor in the power that is determined by an overlap integral between the mode field patterns; in the limit of a very large cavity, this overlap integral recovers the phase-matching condition for (χ(2)) processes. Third, the frequency conversion no longer saturates instead, it peaks (at 100%, with proper design) for a certain critical input power satisfying a resonant condition, and goes to zero if the power is either too small or too large.
Second-harmonic generation in cavities with a single resonant mode at the pump frequency or the harmonic frequency requires much higher power than a doubly resonant cavity, approaching one Watt and/or requiring amplification within the cavity. A closely related case is that of sum-frequency generation in a cavity resonant at the two frequencies being summed. Second-harmonic generation in a doubly resonant cavity, with a resonance at both the pump and harmonic frequencies, has most commonly been analyzed in the low-efficiency limit where nonlinear down-conversion can be neglected, but down-conversion has also been included by some authors.
Here, one can show that not only is down-conversion impossible to neglect at high conversion efficiencies (and is, in fact, necessary to conserve energy), but also that it leads to a critical power where harmonic conversion is maximized. This critical power was demonstrated numerically in a sub-optimal geometry where 100% efficiency is impossible, but does not seem to have been clearly explained theoretically.